This is the final version. Available on open access from EGU via the DOI in this recordSeveral past episodes of rapid carbon cycle and climate change are hypothesised to be the result of the Earth system reaching a tipping point beyond which an abrupt transition to a new state occurs. At the Palaeocene-Eocene Thermal Maximum (PETM) at ∼ 56 Ma and at subsequent hyperthermal events, hypothesised tipping points involve the abrupt transfer of carbon from surface reservoirs to the atmosphere. Theory suggests that tipping points in complex dynamical systems should be preceded by critical slowing down of their dynamics, including increasing temporal autocorrelation and variability. However, reliably detecting these indicators in palaeorecords is challenging, with issues of data quality, false positives, and parameter selection potentially affecting reliability. Here we show that in a sufficiently long, high-resolution palaeorecord there is consistent evidence of destabilisation of the carbon cycle in the ∼ 1.5 Myr prior to the PETM, elevated carbon cycle and climate instability following both the PETM and Eocene Thermal Maximum 2 (ETM2), and different drivers of carbon cycle dynamics preceding the PETM and ETM2 events. Our results indicate a loss of "resilience" (weakened stabilising negative feedbacks and greater sensitivity to small shocks) in the carbon cycle before the PETM and in the carbon-climate system following it. This pre-PETM carbon cycle destabilisation may reflect gradual forcing by the contemporaneous North Atlantic Volcanic Province eruptions, with volcanism-driven warming potentially weakening the organic carbon burial feedback. Our results are consistent with but cannot prove the existence of a tipping point for abrupt carbon release, e.g. from methane hydrate or terrestrial organic carbon reservoirs, whereas we find no support for a tipping point in deep ocean temperature.This work was supported by an EPSRC/ReCoVER Early Career Research Project Award (number: RFFECR 002) and an NERC Studentship to DIAM (number: NE/J500112/1) hosted at Ocean and Earth Science at the University of Southampton, with revised analyses performed at Stockholm Resilience Centre. TML was supported by a Royal Society Wolfson Research Merit Award and the NERC “JET” large grant (NE/N018508/1).